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We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted…

Long-term videomicroscopy and computer-aided statistical analysis were used to determine some characteristic parameters of in vitro cell motility and proliferation in three established cell lines derived from human glioblastoma tumors.…

Tomasetti and Vogelstein (2015a) find that the incidence of a set of cancer types is correlated with the total number of normal stem cell divisions. Here, we separate the effects of standing stem cell number (i.e., organ or tissue size) and…

Cancer cells exhibit increased motility and proliferation, which are instrumental in the formation of tumours and metastases. These pathological changes can be traced back to malfunctions of cellular signalling pathways, and calcium…

Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform…

This paper investigates cells proliferation dynamics in small tumor cell aggregates using an individual based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as…

The homeostasis of epithelial tissue relies on a balance between the self-renewal of stem cell populations, cellular differentiation, and loss. Although this balance needs to be tightly regulated to avoid pathologies, such as tumor growth,…

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor…

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least…

Breakage-Fusion-Bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then `unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the…

A cell-molecular based evolutionary model of tumor development driven by a stochastic Moran birth-death process is developed, where each cell carries molecular information represented by a four-digit binary string, used to differentiate…

Aberrantly regulated cell motility is a hallmark of cancer cells. A hybrid agent-based model has been developed to investigate the synergistic and antagonistic cell motility-impacting effects of three microenvironment variables…

We employ the state-of-the-art molecular dynamics simulations to study the kinetics of phase separation and aging phenomena of segregating binary fluid mixtures imbibed in porous materials. Different random porous structures are considered…

Understanding how microenvironmental heterogeneity influences tumor progression is essential for advancing both cancer biology and therapeutic strategies. In this study, we develop a cellular automata (CA) model to simulate tumor growth…

Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of…

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…

Heterogeneity within tumour cell populations is associated with an increase in malignancy and appears to play an important role during cancer metastasis. Using in silico experiments, we study the interplay between collective behaviours and…

One of many important features of the tumour microenvironment is that it is a place of active Darwinian selection where different tumour clones become adapted to the variety of ecological niches that make up the microenvironment. These…

Motivated by observations of heterogeneous domain structure on the surface of cells, we consider a minimal model to describe the dynamics of phase separation on the surface of a spherical particle. Finite-size effects on the curved particle…

Collective cell movement, characterized by multiple cells that are in contact for substantial periods of time and undergo correlated motion, plays a central role in cancer and embryogenesis. Recent imaging experiments have provided…